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Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics

A Guided Differential Evolution Algorithm for Control Design of Quantum Gates

Shouliang Hu, Hailan Ma, Chunlin Chen

Published Oct 17, 2021• 1 citation
Publisher

Abstract

Constructing high fidelity quantum gates is a key task in quantum information technology. Gradient-based methods (e.g., GRAPE) have been widely used for numerous implementations of quantum gate control tasks but are not practical for in-situ laboratory experiments. In this paper, for the design of optimal control fields for constructing quantum gates, we propose a Guided Differential Evolution (GDE) algorithm. Numerical results verify the effectiveness of the proposed GDE algorithm for the control design of quantum gates with short evolution time and few control pulses.

DOI
10.1109/smc52423.2021.9659044

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Constructing high fidelity quantum gates is a key task in quantum information technology. Gradient-based methods (e.g., GRAPE) have been widely used for numerous implementations of quantum gate control tasks but are not practical for in-situ laboratory experiments. In this paper, for the design of optimal control fields for constructing quantum gates, we propose a Guided Differential Evolution (GDE) algorithm. Numerical results verify the effectiveness of the proposed GDE algorithm for the control design of quantum gates with short evolution time and few control pulses.
In the quest to achieve scalable quantum information processing technologies, gradient-based optimal control algorithms (e.g., grape) are broadly used for implementing high-precision quantum gates, but their performance is often hindered by deterministic or random errors in the system model and the control electronics. In this paper, we show that grape can be taught to be more effective by jointly learning from the design model and the experimental data obtained from process tomography. The resulting data-driven gradient optimization algorithm (d-grape) can in principle correct all deterministic gate errors, with a mild efficiency loss. The d-grape algorithm may become more powerful with broadband controls that involve a large number of control parameters, while other algorithms usually slow down due to the increased size of the search space. These advantages are demonstrated by simulating the implementation of a two-qubit controlled-not gate.
Methods of optimal control are applied to a model system of interacting two-level particles (e.g., spin-half atomic nuclei or electrons or two-level atoms) to produce high-fidelity quantum gates while simultaneously negating the detrimental effect of decoherence. One set of particles functions as the quantum information processor, whose evolution is controlled by a time-dependent external field. The other particles are not directly controlled and serve as an effective environment, coupling to which is the source of decoherence. The control objective is to generate target one- and two-qubit unitary gates in the presence of strong environmentally-induced decoherence and under physically motivated restrictions on the control field. The quantum-gate fidelity, expressed in terms of a novel state-independent distance measure, is maximized with respect to the control field using combined genetic and gradient algorithms. The resulting high-fidelity gates demonstrate the feasibility of precisely guiding the quantum evolution via optimal control, even when the system complexity is exacerbated by environmental coupling. It is found that the gate duration has an important effect on the control mechanism and resulting fidelity. An analysis of the sensitivity of the gate performance to random variations in the system parameters reveals a significant degree of robustness attained by the optimal control solutions.
Methods of optimal control are applied to a model system of interacting two-level particles (e.g., spin-half atomic nuclei or electrons or two-level atoms) to produce high-fidelity quantum gates while simultaneously negating the detrimental effect of decoherence. One set of particles functions as the quantum information processor, whose evolution is controlled by a time-dependent external field. The other particles are not directly controlled and serve as an effective environment, coupling to which is the source of decoherence. The control objective is to generate target one- and two-qubit unitary gates in the presence of strong environmentally-induced decoherence and under physically motivated restrictions on the control field. The quantum-gate fidelity, expressed in terms of a novel state-independent distance measure, is maximized with respect to the control field using combined genetic and gradient algorithms. The resulting high-fidelity gates demonstrate the feasibility of precisely guiding the quantum evolution via the optimal control, even when the system complexity is exacerbated by environmental coupling. It is found that the gate duration has an important effect on the control mechanism and resulting fidelity. An analysis of the sensitivity of the gate performance to random variations in the system parameters reveals a significant degree of robustness attained by the optimal control solutions.
The efficient implementation of quantum computing is contingent upon high-fidelity quantum operations. Nevertheless, the fidelity of these operations is constrained by the precision of quantum system evolution control. The optimization of quantum control pulses is essential for improving the manipulation accuracy of superconducting qubits. Traditional optimization methods, including gradient descent and the gradient ascent pulse engineering algorithm, frequently encounter challenges such as slow convergence and susceptibility to local optima in pulse optimization problems. This study introduces an adaptive open-loop optimization algorithm based on the adaptive moment estimation (Adam) optimizer, capitalizing on the benefits of momentum and adaptive learning rate adjustments inherent in Adam. We conduct experimental analysis on the algorithm’s hyperparameters to achieve optimal solutions with a higher fidelity range at a faster convergence speed, effectively improving the fidelity and optimization efficiency of quantum gate operations. Through numerical simulations on the QuTiP platform, we validate the excellent performance of the Adam algorithm in quantum gate optimization. In optimizing the X and SWAP gates, its fidelity improved by 0.03% and 0.0016%, respectively, compared to the GRAPE algorithm. Compared to the CRAB method, the initial convergence speed of the Adam method increased fivefold, enabling it to achieve the target fidelity more rapidly. Future research will investigate closed-loop optimization strategies, utilizing feedback derived from the fidelity results of actual quantum computers to further augment quantum control performance
Superconducting nanoelectrical circuits are promising candidates for the physical implementation of the basic building block of a quantum computer, the qubit. We investigate how optimal control theory can be applied to optimize the dynamics of Josephson qubits. For the example of the charge qubit, several numerical methods are employed to search for external control fields which, by current technology, are realistic and induce the desired unitary time evolution within the system (i.e. the desired gate operation) as faithfully as possible in presence of dissipation, decoherence and leakage. Associated calculations which model the environment microscopically are time-intensive so that parallel computing methods are beneficial in the sampling over control fields. In particular, we discuss the performance of differential-evolution-algorithm based optimizations on a cluster. Using a simpler Lindblad model for environmental effects, we compare the performance of a conjugate-gradient approach to that of a genetic algorithm.
Robust control design for quantum systems has been recognized as a key task in quantum information technology, molecular chemistry and atomic physics. In this paper, an improved differential evolution algorithm of msMS_DE is proposed to search robust fields for various quantum control problems. In msMS_DE, multiple samples are used for fitness evaluation and a mixed strategy is employed for mutation operation. In particular, the msMS_DE algorithm is applied to the control problem of open inhomogeneous quantum ensembles and the consensus problem of a quantum network with uncertainties. Numerical results are presented to demonstrate the excellent performance of the improved DE algorithm for these two classes of quantum robust control problems. Furthermore, msMS_DE is experimentally implemented on femtosecond laser control systems to generate good signals of two photon absorption and control fragmentation of halomethane molecules CH2BrI. Experimental results demonstrate excellent performance of msMS_DE in searching effective femtosecond laser pulses for various tasks.